Assuming uniqueness condition,
an optimal \(O(n\log n)\) -step discrete mixing time was proved for the Glauber dynamics on graphs with bounded maximum degree [1]}, [2]}, and very recently on all graphs [3]}.
Furthermore,
cond:main holds easily for the Ising model for any \(1-O\left(\frac{1}{\Delta }\right)\le \beta \le 1+O\left(\frac{1}{\Delta }\right)\) .
Consequently, we have the following parallel Ising sampler.
